When you're light 300+ there's a small chance of them being 310. When you're 311+ there's a very high chance of them being 310. So always equip your best setup before decrypting.
3oC just increases the chance that the next ultra you beat will drop an exotic. If it doesn't, then the next use makes it even more likely.
Apparently the best way to get guaranteed exotics is to beat 3 strikes in a row (exclude Psion Flayers from the count), popping a 3oC during the third one. Should drop an exotic. Then go to orbit and repeat. Quite often get an exotic from the raid if you use a 3oC before Warpriest, Golgoroth and Oryx's shade phase.